Calculus problem with Summation I think?

In summary, there is a line of buckets numbered 0, 1, 2... with an elephant behind each bucket. Peanuts start falling into bucket 0 at a rate of one per second for 2^12 seconds. Whenever 5 peanuts accumulate in a bucket, the elephant behind it eats four and places the remaining one in the bucket to the left. After all the peanuts have been eaten, the question is how many peanuts remain in each bucket. This problem is similar to addition in arithmetic base 5.
  • #1
harry2331
1
0

Homework Statement


A line of buckets numbered 0,1,2... extends indefinitely to the left with an elephant behind each bucket. Initially, all of the buckets are empty but then peanuts start falling into bucket 0 at a rate of one per second for 2^12 seconds. Whenever 5 peanuts accumulate in a bucket the elephant behind the bucket picks up all five, eats four, and places the remaining one in the bucket immediately to the left. When there are no more peanuts to be eaten, how many peanuts remain in each bucket?
 
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  • #2
No, it's not a calculus problem. Try working it out for small numbers of peanuts. Doesn't it remind you of addition in arithmetic base 4?
 
  • #3
Sorry, typo. Make that base 5.
 

What is a summation in calculus?

A summation, also known as a series, is a mathematical notation used to represent the addition of a sequence of numbers or terms. It is denoted by the Greek letter sigma (∑) and is often used in calculus to represent the total area under a curve.

How do you solve a summation in calculus?

To solve a summation in calculus, you need to follow these steps:

  1. Identify the pattern of the summation, which can be arithmetic, geometric, or a combination of both.
  2. Find the formula for the pattern using algebraic manipulation.
  3. Determine the number of terms in the summation and plug it into the formula.
  4. Calculate the sum of the terms using the formula.

What is the difference between a finite and infinite summation in calculus?

A finite summation in calculus has a fixed number of terms, while an infinite summation has an infinite number of terms. Finite summations can be solved using the steps mentioned above, while infinite summations require more advanced techniques such as limits and convergence tests.

How is a summation used in calculus?

In calculus, summations are used to represent the total area under a curve, which is known as integration. They are also used to find the sum of an infinite sequence of numbers, which is known as a series. Additionally, summations are used to calculate the average rate of change of a function over a given interval.

What are some common types of summations in calculus?

Some common types of summations in calculus include:

  • Arithmetic summations: where the difference between consecutive terms is constant.
  • Geometric summations: where the ratio between consecutive terms is constant.
  • Telescoping summations: where most terms in the summation cancel out, leaving only a few remaining terms to be added.
  • Power series summations: where the terms are raised to a power.

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